Question

Three newly wed couples are dancing at a function. If the partner is selected at random the chance that all the husbands are not dancing with their own wives is

• A. $\frac{1}{3}$
• B. $\frac{1}{6}$
• C. $\frac{5}{6}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{5}{6}$

Required probability $=$ (Probability that only $1$ husband dances with his wife) + (Probability that only $2$ husbands dance with their wives) + (Probability that $no$ husband dances with his wife) $=1-$(Probability that all husbands dance with their wives).
Therefore, the probability $=1-\frac{1}{3!}=\frac{5}{6}$